Question

An algebra 2 test has 5 multiple choice questions with four choices with one correct answer each. If we just randomly guess on each of the 5 questions, what is the probability that you get at least 1 question correct

Answer 1

0.7627

Explanation:

This is a binomial probability problem

Given :

Number of trials, n = 5

p = number of correct option / total options = 1/4 = 0.25

q = 1 - p = 1 - 0.25 = 0.75

Using the binomial probability relation :

P(x = x) = nCx * p^x * q^(n-x)

Getting atleast 1 correct :

P(x ≥ 1) = p(x = 1) + p(x = 2) + p(x = 3) + p(x =4) + p(x = 5)

P(x =1) = 5C1 * 0.25^1 * 0.75^4 = 0.3955

P(x =2) = 5C2 * 0.25^2 * 0.75^3 = 0.2637

P(x =3) = 5C3 * 0.25^3 * 0.75^2 = 0.0879

P(x =4) = 5C4 * 0.25^4 * 0.75^5 = 0.0146

P(x =5) = 5C5 * 0.25^5 * 0.75^0 = 0.0009

P(x ≥ 1) = 0.3955 + 0.2637 + 0.0879 + 0.0146 + 0.0009 = 0.7627

P(x ≥ 1) = 0.7627